# Population-Level Generative Modeling for Ranking Data

arXiv: https://arxiv.org/abs/2608.08422 · HTML: https://mlsanity.com/paper/2608.08422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 58 references that are in the map.
- First posted on arXiv 9 Aug 2026.

## Builds on (most cited first, 30 of 40)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Eliciting Human Preferences with Language Models](https://mlsanity.com/paper/2310.11589/) (2023)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularization](https://mlsanity.com/paper/2405.16455/) (2024)
- [On Softmax Direct Preference Optimization for Recommendation](https://mlsanity.com/paper/2406.09215/) (2024)
- [Spectral Method and Regularized MLE Are Both Optimal for Top-K Ranking](https://mlsanity.com/paper/1707.09971/) (2017)
- [Categorical Flow Matching on Statistical Manifolds](https://mlsanity.com/paper/2405.16441/) (2024)
- [Scaling Laws For Dense Retrieval](https://mlsanity.com/paper/2403.18684/) (2024)
- [Flow matching achieves almost minimax optimal convergence](https://mlsanity.com/paper/2405.20879/) (2024)
- [Ranking Inferences Based on the Top Choice of Multiway Comparisons](https://mlsanity.com/paper/2211.11957/) (2022)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Scalable Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.13472/) (2020)
- [Learning Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/1603.07323/) (2016)
- [Optimal Design for Human Preference Elicitation](https://mlsanity.com/paper/2404.13895/) (2024)
- [Optimal Full Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2101.08421/) (2021)
- [Theoretical guarantees in KL for Diffusion Flow Matching](https://mlsanity.com/paper/2409.08311/) (2024)
- [Optimal Scheduling of Dynamic Transport](https://mlsanity.com/paper/2504.14425/) (2025)
- [Learning from Comparisons and Choices](https://mlsanity.com/paper/1704.07228/) (2017)
- [Preference Completion: Large-scale Collaborative Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1507.04457/) (2015)
- [Towards Large-scale Generative Ranking](https://mlsanity.com/paper/2505.04180/) (2025)
- [Fundamental Limits of Game-Theoretic LLM Alignment: Smith Consistency and Preference Matching](https://mlsanity.com/paper/2505.20627/) (2025)
- [A unified analysis of likelihood-based estimators in the Plackett--Luce model](https://mlsanity.com/paper/2306.02821/) (2023)
- [Preference Diffusion for Recommendation](https://mlsanity.com/paper/2410.13117/) (2024)
- [SQL-Rank: A Listwise Approach to Collaborative Ranking](https://mlsanity.com/paper/1803.00114/) (2018)
- [Learning Mixtures of Permutations: Groups of Pairwise Comparisons and Combinatorial Method of Moments](https://mlsanity.com/paper/2009.06784/) (2020)

## Abstract (arXiv)

Ranking data arise in scientific and machine learning applications, including recommendation systems, information retrieval, voting, marketing, and AI preference ranking from human feedback. Existing statistical work has primarily focused on inference tasks such as preference estimation, rank aggregation, and ranking prediction. However, generating realistic synthetic rankings from an observed population is important for privacy-preserving data sharing, benchmark construction, simulation, and uncertainty quantification. This task is challenging because rankings are high-dimensional combinatorial objects with non-Euclidean dependence structures, while ranking populations often exhibit substantial preference heterogeneity. We propose a framework for population-level generative modeling through a latent preference simplex embedding. It estimates a low-dimensional latent preference simplex through a likelihood-based ranking model, leverages flow matching to learn the population distribution of latent preferences, and generates new rankings through the fitted probabilistic ranking model. We show that ranking generation admits an oracle reduction to latent distribution learning and derive finite-sample generative guarantees that clarify how the number of items, ranking length, and latent dimension affect accuracy. Experiments on synthetic and real datasets demonstrate improved population-level fidelity and provide a statistically interpretable representation of preference heterogeneity.